Velocity anisotropy, which is known as the directional dependency of velocities, is important in subsurface imaging and characterization. Most elasticity theories consider an isotropic medium as their main assumption for addressing the problems in the field of reservoir geophysics. This assumption is challenged by the reality of the subsurface, which could be made up of structures such as beds and fractures and which has gone through a complex geological history. These factors can make the subsurface of the Earth deviate significantly from the isotropic assumption used in the routine algorithms and approaches.
In general, four classes of anisotropy are defined that range from a completely isotropic medium (with two elastic constants) to a completely anisotropic medium (with 21 elastic constants). The four classes refer to specific conditions where the number of elastic stiffness constants can be reduced. The four classes are named Cubic with 3 independent elastic constants, Transverse Isotropic (TI) with 5 independent elastic constants, Orthorhombic with 9 independent elastic constants and Monoclinic with 13 independent elastic constants. A TI medium provides the closest description of sedimentary rock.
Conventionally, anisotropy in the context of isotropic approaches is handled using Thomsen parameters and approximation. Thomsen suggested three parameters to correct for anisotropy effects in weak-anisotropy mediums. These parameters, ε, δ and γ, are now used regularly in all reservoir geophysics disciplines to address anisotropy effects. However, calculation of the Thomsen parameters requires information such as laboratory data or well tracks in different directions compared with the symmetry axis which are expensive to apply in practice. Therefore, the need still exists to improve cheaper methods for calculating anisotropy parameter in the form of stiffness tensor or Thomsen parameters in a TI subsurface.